STATEMENT OF THE PROBLEMConsider the equation u xx + yu yy + αu y = 0, α<−1/2,in the mixed domain D whose elliptic part D 1 coincides with the entire upper half-plane and whose hyperbolic part consists of two infinite triangles D 2 and D 3 , where D 2 is bounded by the characteristics y = 0 and x − 2 √ −y = 0 and D 3 is bounded by the characteristics y = 0 andFor negative values of the parameter α, Eq.(1) was considered by numerous authors (e.g., see [1][2][3][4][5]), who mainly dealt with the Tricomi and Gellerstedt problems as well as some modifications of these problems. In the present paper, we consider a problem that is an analog of the Frankl problem for parameter values α such that 2α is not an integer.By n and m we denote positive integers satisfying the inequalities −1/2 < α + n = α 0 < 1/2 and 0 < 2α + m − 1 = δ < 1. Obviously, m = 2n + 2 and δ = 2α 0 + 1 for −1/2 < α 0 < 0, and m = 2n + 1 and δ = 2α 0 for 0 < α 0 < 1/2. Problem F α . In the domain D, find a function u(x, y) with the following properties:(1) u(x, y) belongs to the class(2) the estimatesare valid as R → +∞, where R 2 = x 2 + 4y and (x, y) ∈ D 1 ;(3) u(x, y) belongs to C 2 (D 1 ∪ D 2 ∪ D 3 ) and satisfies Eq. (1) in D 1 ∪ D 2 ∪ D 3
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